man zlags2 (Fonctions bibliothèques) - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
NAME
ZLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
SYNOPSIS
- SUBROUTINE ZLAGS2(
- UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )
- LOGICAL UPPER
- DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV
- COMPLEX*16 A2, B2, SNQ, SNU, SNV
PURPOSE
ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV )
Q = ( CSQ SNQ )
( -CONJG(SNQ) CSQ )
Z' denotes the conjugate transpose of Z.
The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.
ARGUMENTS
- UPPER (input) LOGICAL
- = .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular. - A1 (input) DOUBLE PRECISION
- A2 (input) COMPLEX*16 A3 (input) DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
- B1 (input) DOUBLE PRECISION
- B2 (input) COMPLEX*16 B3 (input) DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
- CSU (output) DOUBLE PRECISION
- SNU (output) COMPLEX*16 The desired unitary matrix U.
- CSV (output) DOUBLE PRECISION
- SNV (output) COMPLEX*16 The desired unitary matrix V.
- CSQ (output) DOUBLE PRECISION
- SNQ (output) COMPLEX*16 The desired unitary matrix Q.